Well, as a graphic designer I believe that we should aim for something simple, easy to remember, and inspired by something related to the engine/name.

My thinking is a Mobius Stripe, also known to be the used as the recycle symbol shape.

The colours are the basic colours used on the old Japanese covers, mostly Sonic, Tails and Knuckles colours too, the shading is inspired by Sonic Colours Logo, and the font is just a nice Art-deco-like font I found.

It's really basic but this thing was made in 5 minutes in a hurry, I have a Japanese exam in an hour or so

Edit; added a simplier variation, more accord to current design trends. Less bevels, less stuff.

Maybe no one else thinks it matters, but perhaps the top strip should be the blue one? I'm thinking in terms of prioritising the colours according to character. If it were me, I'd've tried top=blue, left=yelloworange Tailsish, right=red.

Just throwing an idea out here: what if you made the strip a *lot* thinner, and put the text "Mobius Engine" at the centre of it? See what that looks like..

The words are too thick to fit like it should, however I made a thinner version of it:

The question would then be, does it need to be that font that you're using here for this?

This is kind've the idea I was thinking of [below], but perhaps make the black font a little more interesting. I suppose you can ignore this idea if you're planning to use the strip itself without any text on it to be used as an 'icon' of some sort?

Also, how would it look if it had shadows on the bends of the strips (to give it a slightly more 3D look)? Just a wonderment..

Ignore the obviously-wrong lighting, 'tis merely the result of rotating Elratauru's image instead of trying to recreate it. Also, the drop shadow on the text probably doesn't need to be there, I was experimenting and forgot to remove it when I was done. But to be honest, I mainly did this for the sake of using a font with a higher x-height. Initially, I was going to use Steelfish, but I discovered it has some pretty annoying alignment issues, which saddens me because I like the overall design of the font.

The font is a bit debatable I think, and honestly, having Mobius Engine right in the middle of the logo kinda looks like crap. The mobius strip is kinda the insignia here, placing text right on top of it draws attention solely to the text, not the insignia.

RE: Font. I'd say the current font and letter arrangement fits well, especially if we go for block letters.